On monotonicity conditions for mean field games
On monotonicity conditions for mean field games
复制标题
平均场博弈的单调性条件
DOI：
10.1016/j.jfa.2023.110095
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发表时间：
2023
影响因子：
1.7
通讯作者：
Mészáros, Alpár R.
中科院分区：
文献类型：
--
作者：
Graber, P. Jameson;Mészáros, Alpár R.
在本文中，我们提出了两个新的单调性条件，可以作为纳什均衡的唯一性的充分条件的平均场游戏。在这项研究中，我们的目标forconditional uniqueness是独立的时间范围的长度，规则性的开始分布的代理商，或正规化效果的非退化特质噪声。通过大量简单的例子，我们证明了这些新的条件不仅相互之间是二分法，而且与文献中两个被广泛研究的单调性条件Lasry-Lions单调性和位移单调性条件也是二分法.
In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim forunconditional uniquenessthat is independent of the length of the time horizon, the regularity of the starting distribution of the agents, or the regularization effect of a non-degenerate idiosyncratic noise. Through a rich class of simple examples we show that these new conditions are not only in dichotomy with each other, but also with the two widely studied monotonicity conditions in the literature, the Lasry–Lions monotonicity and displacement monotonicity conditions.